<p><b>Abstract</b>—One limitation on the operating speed of electronic circuits is the rate at which the packaging can dissipate heat. In CMOS technology, the heat generated by a processor is approximately proportional to its clock rate. This paper examines the idea of using a variable-speed processor (VSP) that can be operated at a high clock speed, and then slowed down to a lower speed before heat accumulation destroys the circuit. Under a workload consisting of bursts of work alternating with idle periods (corresponding to cache misses or other delays), this results in a higher average operating speed. This paper shows the optimality of a bang-bang control for the clock rate. It also examines an easier-to-implement policy that estimates the junction temperature through an upper bound, and uses this to control the clock rate. Closed-form expressions are derived for the mean rate of instructions executed by a VSP using each control method. Numerical studies show that both policies give substantial improvements in performance over a single speed processor. Furthermore, the studies suggest that a VSP with a maximum clock rate of 2-4 times that of the single speed processor would suffice to obtain the bulk of the performance improvement. In many cases, the average throughput gain is on the order of 40-60%, without exceeding thermal limits.</p>